Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Meta-Analysis in Clinical Trials*

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

/pdf/latent-dirichlet-allocation-4gmscb06en.pdf

Latent dirichlet allocation

Unit nonresponse and item nonresponse both occur frequently in surveys. Unit nonresponse is customarily handled by weighting adjustment, whereas item nonresponse is usually treated by some form of imputation. In particular, deterministic or stochastic imputation is often used to assign values for missing item responses. We provide an account of some recent work on jackknife variance estimation based on adjusted imputed values, using only a single imputation and hence a single completed data set. We also present linearized versions of the jackknife variance estimators. We study both stratified simple random sampling and stratified multistage sampling. Existing computer programs for jackknife and linearization variance estimation can be modified to implement the proposed variance estimators without requiring the creation and permanent retention of supplemental data sets. But for secondary analyses, the completed data set must include information on response status for each item as well as on the imputation class.

On Variance Estimation With Imputed Survey Data: Comment

The Department of Education’s table “State Education Statistics” reports mean test scores by state and mean resource inputs by state. The means are calculated from quite different groups of students, a process we callinconsistent aggregation. We investigate the bias in regression coefficients caused by inconsistent aggregation, first using theoretical calculations, and then by artificially aggregating data from the High School and Beyond sample.

Discussion of “on State Education Statistics”: A Difficulty with Regression Analyses of Regional Test Score Averages

The sample multiple correlation coefficient is often used to compare sets of independent variables with respect to how well they predict the future values of a dependent variable, Y. If the data are partially missing, the comparison often should reflect not only how correlated the predictors are with Y but also how likely they are to be observed. Thus, an independent variable that is highly correlated with Y but also is often missing is not as useful a predictor of future Y values as a less correlated but always observed independent variable. A generalization of the multiple correlation coefficient is defined which is appropriate when there are missing values but is identical to the multiple correlation coefficient when there are no missing values. An example of its use is presented.

https://www.jstor.org/stable/info/1267523

Comparing Regressions When Some Predictor Values Are Missing

Causation is a topic that many statisticians address indirectly in their applied work when conducting randomized experiments or observational studies for treatments. Remarkably few statisticians, however, have addressed the topic in their own writing or theoretical research. I.J. Good is one of these few (e.g., Good, 1961, 1971, 1972, 1980a, 1980b, 1983, 1988), and consequently this brief review of modes of statistical inference for causal effects seems appropriate for a volume honoring Jack’s extensive and creative contributions to statistics.

Formal modes of statistical inference for causal effects

In the previous companion paper we showed that high power RF processing (HPP) is an effective technique to reduce field emission in superconducting cavities, so higher accelerating gradients can be reached. In this work we show improved understanding of the mechanisms at work when field emitters process. Thermometry measurements of the outer wall of single-cell cavities reveal the field emission from localized sites and also the reduction in field emission by processing. Subsequent scanning electron microscope (SEM) examination of the RF surface at the emission/processed sites reveals 5–10 μm sized molten craters, micron sized molten particles of foreign elements, and sub-mm sized spots shaped like starbursts. These features indicate that processing occurs through a violent melting/vaporization phenomenon. A “model” for RF processing is presented based upon the experimental evidence, both from this study and from others.

Donald B. Rubin

Papers

On Variance Estimation With Imputed Survey Data: Comment

Discussion of “on State Education Statistics”: A Difficulty with Regression Analyses of Regional Test Score Averages

Comparing Regressions When Some Predictor Values Are Missing

Formal modes of statistical inference for causal effects

Microscopic investigation of high gradient superconducting cavities after reduction of field emission